Dnestrovskij Yu.N. Self-Organization of Hot Plasmas: The Canonical Profile Transport Model

Springer International Publishing, 2015. — 134 p. — ISBN: 978-3-319-06801-5, 978-3-319-06802-2.This book is devoted to the problem of confinement of energy and particles in tokamak plasmas. Although the first tokamaks were constructed more than half a century ago, large efforts will still be needed before a detailed description of transport in these devices will be a reality. So far, high hopes for a description of transport in tokamaks using huge multidimensional gyro-kinetic codes did not materialize. Growing attention is now focusing on the idea of self-organization in plasmas. The fusion community rejected a long ago the fundamental concept of a local connection between transport coefficients and plasma parameters. The idea that the fundamental nature of transport in fusion plasmas is dual, begins now to gain momentum: profiles of pressure and temperature are determined in main by the magnetic configuration and in a lesser extent by the energy and particle fluxes.In this monograph the author presents the Canonical Profile Transport Model or CPTM as a rather general mathematical framework to simulate plasma discharges.The description of hot plasmas in a magnetic fusion device is a very challenging task and many plasma properties still lack a physical explanation. One important property is plasma self-organization.It is very well known from experiments that the radial profile of the plasma pressure and temperature remains rather unaffected by changes of the deposited power or plasma density. The attractiveness of the CPTM is that it includes the effect of self-organization in the mathematical model without having to recur to particular physical mechanisms.The CPTM model contains one dimensional transport equations for ion and electron temperatures, plasma density and toroidal rotation velocity. These equations are well established and in fact are essentially a reformulation the laws of energy, particle and momentum conservation. But the expressions for the energy and particle fluxes, including certain critical gradients, are new. These critical gradients can be determined using the concept of canonical profiles for the first time formulated in great detail in the book. This concept represents a totally new approach to the description of transport in plasmas. Mathematically, the canonical profiles are formulated as a variational problem. To describe the temporal evolution of the plasma profiles, the Euler equation defining the canonical profiles is solved together with the transport equations at each time step. The author shows that in this way it is possible to describe very different operational scenarios in tokamaks (L-Mode, H-Mode, Advanced Modes, Radiating Improved Modes etc…), using one unique principle.The author illustrates the application of this principle to the simulation of plasmas on leading tokamak devices in the world (JET, MAST, T-10, DIII-D, ASDEX-U, JT-60U). In all cases the small differences between the calculated profiles for the ion and electron temperatures and the experimental is rather confirm the validity of the CPTM. In addition, the model also describes the temperature and density pedestals in the H-mode and non steady-state regimes with current and density ramp up. The proposed model therefore provides a very useful mathematical tool for the analysis of experimental results and for the prediction of plasma parameters in future experiments.Variational Principles for Canonical Profiles in a Tokamak
A Possible Approach to the Canonical Profiles in Stellarators
Theoretical Limitations for Scaling Laws and Transport Coefficients
Linear Version of the Canonical Profiles Transport Model (CPTM)
Nonlinear Version of the Canonical Profiles Transport Model (CPTM) for Improved Confinement Regimes